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Relaxing Constraints on Dark Matter Annihilation Near the Supermassive Black Hole in M87

T0 review · 1 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read If M87's dark halo is cored, its central density spike contributes almost nothing to dark matter annihilation, relaxing the galaxy's gamma-ray constraints.

desk verdict Clean conditional calculation: with M87's 91-kpc Burkert core, the SMBH spike is a non-factor for annihilation fluxes, but the community should still demand a cored-vs-cuspy model comparison before discarding M87 as a WIMP probe. read the letter →

arxiv 2411.18751 v2 pith:LZCLIMOX submitted 2024-11-27 hep-ph

Mehrdad Phoroutan-Mehr , Hai-Bo Yu This is my paper · ORCID
classification hep-ph
keywords darkmatterannihilationdensityspikeM87BurkertprofileSommerfeldenhancementJ-factorgamma-rayconstraintsself-interacting
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that M87's black-hole density spike does not dramatically boost dark matter annihilation signals if the galaxy's dark halo is cored rather than cuspy. It adopts the Burkert profile fitted to recent kinematics of stars, globular clusters, and satellite galaxies, and computes velocity-dependent annihilation factors with and without Sommerfeld enhancement. The smooth halo dominates: the $J$-factor is about $8\times10^{17}\,\mathrm{GeV^2\,cm^{-5}}$, while the spike $Q$-factor is about $6\times10^{10}\,\mathrm{GeV^2\,cm^{-5}}$, so the spike is negligible. The resulting gamma-ray fluxes are several orders of magnitude below M87 upper limits, meaning the constraints are far weaker than in the widely used NFW spike analysis.

What carries the argument

The argument runs on the ratio of two velocity-weighted line-of-sight integrals: the $J$-factor for the smooth Burkert halo and the $Q$-factor for the spike, which together set the annihilation flux through $d^2\Psi/dE_\gamma d\Omega \propto J(\Omega)+Q(\Omega)$. Both are evaluated with an isotropic Maxwell-Boltzmann velocity distribution truncated at the escape velocity, with Sommerfeld enhancement factors for s- and p-wave annihilation folded into the integrals. The decisive comparison is $\bar J\sim 8\times10^{17}\,\mathrm{GeV^2\,cm^{-5}}$ versus $\bar Q\sim 6\times10^{10}\,\mathrm{GeV^2\,cm^{-5}}$ for the $r^{-7/4}$ spike, a ratio of $10^7$ that makes the spike irrelevant.

What would settle it

Measure M87's inner dark-matter logarithmic slope $\gamma$ below roughly $30\,\mathrm{pc}$ with kinematic tracers: a detection of $\rho\propto r^{-1}$ (cuspy) rather than $\rho\simeq$ constant (cored) would raise the spike normalization by orders of magnitude, pushing the projected fluxes toward or above the upper limits derived from [6] and overturning the claimed relaxation.

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Extended reading notes

Core claim

For a cored Burkert halo with central density $\rho_0=6.94\times10^6\,M_\odot\,\mathrm{kpc}^{-3}$, scale radius $r_0=91.2\,\mathrm{kpc}$, and black-hole influence radius $r_{\rm in}=27.8\,\mathrm{pc}$, the dark matter spike near M87's supermassive black hole contributes negligibly to annihilation signals. The smooth halo gives $\bar J\sim 8\times10^{17}\,\mathrm{GeV^2\,cm^{-5}}$; the spike, modeled with slope $r^{-7/4}$ for Coulomb-like self-interactions, gives $\bar Q\sim 6\times10^{10}\,\mathrm{GeV^2\,cm^{-5}}$, seven orders of magnitude smaller. The conclusion also holds for a steeper $r^{-9/4}$ collisionless spike and for a larger influence radius of $136\,\mathrm{pc}$. For a light-mediator dark matter model with s- and p-wave annihilation and Sommerfeld enhancement, the projected gamma-ray fluxes are several orders of magnitude below the upper limits derived from [6]; a self-consistent SIDM halo that includes the baryonic potential raises the flux by a factor of only $1.3$--$2$ but still leaves it well below the limits.

Load-bearing premise

The load-bearing premise is that M87's dark halo follows the cored Burkert profile of Eq. (1) with $\rho_0=6.94\times10^6\,M_\odot\,\mathrm{kpc}^{-3}$ and $r_0=91.2\,\mathrm{kpc}$ all the way down to the black-hole radius of influence $r_{\rm in}=27.8\,\mathrm{pc}$; if the inner profile is cuspy instead, the spike can dominate and the constraints tighten.

Editorial extensions

If this is right

  • M87's gamma-ray upper limits would no longer rule out thermal-relic WIMPs or light-mediator models if the halo is cored.
  • The spike contributes negligibly, so future M87 analyses should base constraints on the smooth-halo $J$-factor rather than the spike $Q$-factor.
  • The NFW-based spike model of [6] gives a $Q$-factor $10^5$ times the smooth $J$-factor, so the same observational limits yield vastly different cross-section bounds depending on the assumed halo profile.
  • An SIDM halo that includes the baryonic potential raises predicted fluxes by only a factor of $1.3$--$2$, leaving them far below the observational upper limits.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The relaxation is empirical, not model-independent: if future kinematic data inside roughly $30\,\mathrm{pc}$ favor a cusp, the old strong M87 bounds would come back with the same calculation.
  • Since the spike's $Q$-factor is negligible, M87's black-hole spike is not the right target for probing light-mediator annihilation; the observable signal is the extended smooth-halo emission, which requires different angular integration and background treatment.
  • The same $J/Q$ comparison suggests that other giant ellipticals with kinematically inferred cored halos may have overestimated black-hole spike constraints until their inner slopes are measured.
  • A direct test is to measure the inner logarithmic density slope of M87 below $\sim30\,\mathrm{pc}$; a cuspy slope near $\gamma=1$ would flip the paper's central conclusion.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 6 minor

Summary. The paper recalculates the dark matter annihilation J- and Q-factors for M87 using a Burkert cored halo profile taken from De Laurentis & Salucci (2022), combined with an SIDM-motivated density spike of slope 7/4 (and, for comparison, a collisionless cored-halo spike of slope 9/4). A light-mediator dark matter model is adopted, and the velocity-dependent Sommerfeld enhancement is included in the J- and Q-factor computations. The central numerical result is that, for the cored Burkert halo, the smooth halo contribution dominates over the spike contribution by roughly seven orders of magnitude, so the predicted gamma-ray fluxes are several orders of magnitude below the M87 upper limits used by Lacroix et al. (2015). The paper also constructs a self-interacting dark matter halo model including baryonic effects and shows that the conclusion persists.

Significance. If the assumed cored Burkert profile is the correct description of M87's dark matter halo, the paper significantly weakens previously claimed M87 spike constraints on dark matter annihilation and identifies the halo-profile choice as the dominant uncertainty in such constraints. The calculation is transparent, the inputs are clearly stated, and the paper includes useful robustness checks: varying the spike radius from 27.8 pc to 136 pc and the spike slope from 7/4 to 9/4 does not change the conclusion that the smooth halo dominates. The SIDM halo model in Sec. VI is an additional strength, as it shows that a self-consistent cored halo with baryonic contraction still leaves the predicted fluxes far below the observational limits. The main limitation is that the cored profile is adopted rather than established from the kinematic data; the paper does not quantify how strongly the data of Oldham & Auger favor a core over a cusp.

major comments (1)
  1. [Sec. II and Sec. V] The central claim that the M87 annihilation constraints are relaxed is conditional on the Burkert cored profile of Eq. (1) being the true dark matter halo down to r_in = 27.8 pc. The manuscript adopts the best-fit values rho0 = 6.94e6 M_sun kpc^-3 and r0 = 91.2 kpc from Ref. [16] without reporting the fit quality, the parameter uncertainties, or a model comparison against cuspy halos. Since Ref. [15] explicitly fit four halo models including both cored and cuspy families, the paper should either quantify the support for the cored solution (e.g., by reporting likelihood or AIC-type comparisons from the original fits, or by performing a simple comparison with an NFW profile fit to the same mass-profile data) or explicitly reframe the title and conclusions as a conditional sensitivity study. As it stands, the conclusion that constraints are "relaxed" is a proof of principle for a cored halo rather than a demonstration that M87 no longer constrains dark matter annihilation.
minor comments (6)
  1. [Eq. (20)] The notation in Eqs. (14)-(16) is inconsistent: Q(Omega) in Eq. (16) is written as a volume integral divided by D^2, which represents the angle-integrated Q (up to the appropriate 4 pi factor), while Eq. (14) adds it to the per-solid-angle J(Omega). Please clarify that the final flux is computed from Jbar and Qbar integrated over the observation window, and define Q(Omega) consistently throughout.
  2. [Sec. IV, after Eq. (20)] There is a typo in the sentence defining the power-law slope: "rho_sp propto gamma^{-(3+a)/4}" should read "rho_sp propto r^{-(3+a)/4}".
  3. [Sec. II, Eq. (5)] The phrase "constant light-to-mass ratio" should be "constant mass-to-light ratio".
  4. [Sec. V] The text "fixed by the relict density constraint" should read "relic density constraint".
  5. [Sec. VI] The SIDM model fit is described qualitatively ("after several trials", "fits the data well"). Please provide a quantitative measure of the fit, such as the chi^2 or residual scatter relative to the mass-profile data points in Fig. 4, and specify the range of mass-to-light ratio and cross section explored.
  6. [Fig. 3] Please specify the exact origin of the black "Upper Limits" curve: whether it is the observed Fermi-LAT flux upper limit from Ref. [60] as converted in Ref. [6], and over which energy range the limit applies.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the relaxation claim is a conditional calculation built on an externally fitted Burkert halo and standard spike profiles.

full rationale

The paper's central claim is an if-then calculation: if M87's dark matter halo follows the Burkert profile with the best-fit parameters of De Laurentis & Salucci (rho0 = 6.94e6 Msun/kpc^3, r0 = 91.2 kpc), then the spike contribution to the J and Q factors is negligible and the predicted annihilation fluxes lie below the M87 upper limits. The halo input is taken from an external kinematic fit [16], the spike slope gamma_sp = (3+a)/4 is taken from Shapiro & Paschalidis [13], the smooth-halo/spike junction in Eq. (8) is a standard construction, and the upper limits are taken from Lacroix et al. [6]. Equations (19)-(20) are then direct line-of-sight and volume integrals; the result Q << J follows from the flat inner Burkert density and small spike radius, and it is not used to define or fit any input parameter. The SIDM section is explicitly labeled a fit ('we perform an SIDM fit to the measured total mass profile'), with M/L = 3.5 varied 'after several trials' to match the mass data; this is a fitted input, not a prediction, and the subsequent flux calculation is an independent output used only for comparison with [6]. Self-citations to SIDM core physics and the semi-analytic model are supported by publicly available code and hydrodynamical simulations [64,65], and they are not the load-bearing justification for the cored halo, which rests on the external Burkert fit. The main caveat, that cuspy halos would give different and tighter constraints, is acknowledged by the authors and is a modeling assumption rather than a circular step.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central conclusion rests on the Burkert profile parameters adopted from [16] plus the assumed spike slope. The SIDM halo model in Sec. VI adds several hand-set parameters, namely M/L = 3.5, c = 6, and sigma/m = 0.5 cm^2/g, that are adjusted to match the same mass data the model is meant to reproduce, but this section is a consistency check rather than the central claim.

free parameters (7)
  • Burkert central density rho0 = 6.94e6 Msun kpc^-3
    Taken from De Laurentis and Salucci 2022 fit to M87 kinematics; enters Eq. 1 and scales J as rho0^2.
  • Burkert scale radius r0 = 91.2 kpc
    Taken from the same fit; sets where the density starts to fall and affects the line-of-sight J integration.
  • Spike slope parameter a = a = 4
    Chosen as the maximum value for Coulomb-like SIDM to fix rho_sp proportional to r^-7/4 in Eq. 6; the paper checks r^-9/4 as a variant.
  • Mass-to-light ratio Msph/L* = 8.6 Msun/Lsun
    Used in Eq. 5 for the stellar density in the Jeans equation; adopted from [16].
  • SIDM mass-to-light ratio = 3.5 Msun/Lsun
    Chosen after several trials in Sec. VI to make the semi-analytic SIDM profile fit the observed total mass data; not derived from first principles.
  • SIDM concentration and cross section = c = 6, sigma/m = 0.5 cm^2/g
    Fixed by hand in Sec. VI to reproduce the M87 mass profile; consistent with velocity-dependent SIDM models but not uniquely determined.
  • Mediator and dark matter masses = m_phi = 2 MeV or 1 GeV, m_chi = 10 GeV to 10 TeV
    Example model parameters for the light-mediator benchmark; not fitted to M87 data.
assumptions (6)
  • standard math The Jeans equation relates the velocity dispersion to the density and potential gradients for a spherical steady-state system.
    Invoked in Eq. 3 to compute sigma_h and r_in; a standard tool in galactic dynamics.
  • domain assumption The dark matter velocity distribution is an isotropic Maxwell-Boltzmann distribution truncated at the escape velocity.
    Used in Eqs. 17 and 18 for the J and Q factors; standard but unverified for the M87 spike region.
  • domain assumption The SMBH grew adiabatically and the spike follows the Gondolo-Silk (CDM) or Shapiro-Paschalidis (SIDM) power laws.
    Eq. 6 and Sec. II; the paper notes mergers and stellar heating can soften the slope, citing [33,34], but does not model these effects.
  • domain assumption The Burkert profile with rho0 = 6.94e6 Msun kpc^-3 and r0 = 91.2 kpc describes the smooth M87 halo down to the radius of influence.
    Adopted from [16] in Eq. 1; this is the load-bearing astrophysical input for the central claim.
  • domain assumption The spike density is normalized as rho_sp(r_sp) = rho_B(r_sp) with r_sp = r_in, and the density vanishes inside the marginally bound radius r_m.
    Eqs. 6 through 8; any extra spike suppression would only strengthen the paper's conclusion.
  • ad hoc to paper For a = 4 the self-scattering cross section scales as v^-4, the Coulomb-like limit.
    Chosen as the steepest SIDM spike slope in Eq. 6; not an independent measurement, though the conclusion is checked against a steeper CDM spike.

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Cite this review

Pith. "Pith review of Relaxing Constraints on Dark Matter Annihilation Near the Supermassive Black Hole in M87." pith.science (2026). https://pith.science/paper/LZCLIMOX

@misc{pith2026241118751,
  author       = {Pith},
  title        = {Pith review of: Relaxing Constraints on Dark Matter Annihilation Near the Supermassive Black Hole in M87},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LZCLIMOX}},
  note         = {Machine review of arXiv:2411.18751}
}
read the original abstract

The supermassive black hole at the center of M87 could redistribute dark matter particles within its sphere of influence, creating a high-density region known as a density spike. This spike can significantly enhance dark matter annihilation signals, making M87 a critical target for deriving stringent constraints on annihilation cross sections. In this work, we demonstrate that these constraints are highly sensitive to the choice of the halo density profile for M87. Motivated by recent kinematic studies of M87, we adopt a cored halo model and find that the constraints on dark matter annihilation are significantly relaxed. Specifically, in the cored halo scenario, the smooth part of the halo overwhelmingly dominates the annihilation signals, whereas the commonly-assumed cuspy halo model attributes a major contribution to the spike. We demonstrate this effect using a dark matter model with a light mediator.

Figures

Figures reproduced from arXiv: 2411.18751 by the authors.

Figure 1
Figure 1. FIG. 1. Left: Dark matter density profile of M87 with the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Left: Thermally-averaged s-wave (blue) and p-wave (red) Sommerfeld enhancement factors as a function of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Left: Projected gamma-ray fluxes from s-wave (blue) and p-wave (red) dark matter annihilations [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Left: Total mass profiles from the SIDM (green) and Burkert (blue) halo models, compared to the measurements [15, 16] (data points [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Reviewed August 12, 2026 · model on record in the stance chip above.